2. Chapter 6 Momentum

3. Momentum and Collisions This chapter is concerned with inertia and motion. Momentum helps us understand collisions.

4. Momentum = mass X velocity p = mv Momemtum is a vector

5. Sample Questions Which has more momentum, a 1-ton car moving at 100 km/hr or a 2-ton truck moving at 50 km/hr? Carp = mv = (1 ton)(100km/hr) Truckp = (2 ton)(50 km/hr)

6. Large Momentum Examples:  Huge ship moving at a small velocity  High velocity bullet P = m v

7. Impulse Newton’s Second Law can read  F = ma =m(  v/  t) =(  mv)/(  t) =(  p/  t) Rearranging, Impulse =  p = F  t

8. Sample Question Does a moving object have impulse? Impulse is not a property of the object, but something that it can give or get from an interaction. Notice that it is not motion that gives us an impulse (v) but a change in motion (  v).

9. Sample Question Does a moving object have momentum? Yes, but recall that motion is relative, so the momentum depends on having velocity with respect to the standard of rest.

10. When Force is Limited Apply a force for a long time.  Examples:  Follow through on a golf swing.  Pushing a car. FtFt

11. Make it Bounce p1p1 p 2 = -p 1  p = p 2 - p 1 = -p 1 - p 1 = -2p 1

12. Minimize the Force To minimize force …  Increase  t  catching a ball  Bungee jumping FtFt

13. Maximize Momentum Change Apply a force for a short time.  Examples:  Boxing  Karate FtFt

14. If  F = 0, then impulse =  p = zero, or Momentum is conserved

15. Demonstrations Rocket balloon Cannon Rocket Scooter

16. When can Momentum be Conserved? u Internal forces cannot cause a change in momentum of the system. u For conservation of momentum, the external forces must be zero.

17. COLLISIONS Collisions involve forces internal to colliding bodies. Inelastic collisions - conserve momentum Totally inelastic collisions - conserve momentum and objects stick together Elastic collisions - conserve energy and momentum

18. v = 10v = 0 Before Collision MM p = Mv MM After Collision p = 2Mv’ Mv = 2Mv’ v’ = ½ v v’ = 5 v’

19. Collisions Air Track Link

20. Conserve Energy and Momentum Case 1: Case 2: Equal masses M > M Case 3: M < M Before Collision